560 THE PRINCIPLES OF SCIENCE. [CHAP. 



Archimedes also was so perfectly acquainted with the 

 buoyancy of bodies immersed in water, that he could not 

 fail to perceive the existence of a parallel effect in air. 

 Yet throughout the early middle ages the light of true 

 science could not contend with the glare of the Peripatetic 

 doctrine. The genius of Galileo and Newton was required 

 to convince people of the simple truth that all matter 

 is heavy, but that the gravity of one substance may be 

 overborne by that of another, as one scale of a balance is 

 carried up by the preponderating weight in the opposite 

 scale. It is curious to find Newton gravely explaining 

 the difference of absolute and relative gravity, as if it 

 were a new discovery proceeding from his theory. 1 More 

 than a century elapsed before other apparent exceptions 

 to the Newtonian philosophy were explained away. 



Newton himself allowed that the motion of the apsides 

 of the moon's orbit appeared to be irreconcilable with the 

 law of gravity, and it remained for Clairaut to remove the 

 difficulty by more complete mathematical analysis. There 

 must always remain, in the motions of the heavenly bodies, 

 discrepancies of some amount between theory and obser- 

 vation ; but such discrepancies have so often yielded in past 

 times to prolonged investigation that physicists now regard 

 them as merely apparent exceptions, which will afterwards 

 be found to agree with the law of gravity. 



The most beautiful instance of an apparent exception, is 

 found in the total reflection of light, which occurs when a 

 beam of light within a medium falls very obliquely upon 

 the boundary separating it from a rarer medium. The 

 general law is that when a ray strikes the limit between two 

 media of different refractive indices, part of the light is 

 reflected and part is refracted ; but when the obliquity of 

 the ray within the denser medium passes beyond a certain 

 point, there is a sudden apparent breach of continuity, and 

 the whole of the light is reflected. A clear reason can be 

 given for this exceptional conduct of the light. According 

 to the law of refraction, the sine of the angle of incidence 

 bears a fixed ratio to the sine of the angle of refraction, so 

 that the greater of the two angles, which is always that in 

 the less dense medium, may increase up to a right angle ; 



1 Principia, bk. ii. Prop. 20. Corollaries, 5 and 6. 



